Do parents inherit if their child dies?

Agreed. A parent’s entitlement runs as follows. Where the deceased left a child or a son’s child, each parent takes one sixth; if the surviving children are daughters only, the father takes his sixth and whatever is left over after the fixed shares, because he is also the nearest male residuary. Where there is no child, the mother takes one third and the father takes the remainder. Where two or more brothers or sisters survive — of any kind, and whether they themselves inherit or not — the mother drops from a third to a sixth, and the sixth she loses goes to the father. Ibn Qudama records the mother’s third as a point on which there is no disagreement we know of among the people of knowledge, and the father’s three positions as a matter of consensus. On the number of siblings needed to cut the mother back, the schools hold that two are enough; Ibn Rushd names Malik for that view and the only recorded dissent is Ibn ‘Abbas, who required three — and he is a Companion, not one of the four schools. In Canada the practical point is the contrast: under every provincial intestacy statute a surviving parent normally takes nothing while a spouse or child survives. We checked this point; the schools do not differ on it.

Shared evidence: Surah an-Nisa 4:11 — the sixth for each parent, the mother’s third, and her sixth where there are siblings · Sahih al-Bukhari 6732 — “give the fixed shares to those entitled; what remains goes to the nearest male”, the basis of the father taking the residue.

Not covered by this finding: what happens when a grandfather stands in the father’s place, which is a separate and genuinely disputed question — not yet researched school by school. Treat that as open and ask a scholar of your school.